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October 2, 2025Open Access

The full automorphism groups of the five symmetric (15, 8, 4) -designs

Key Points

The full automorphism group of the (15,8,4)-design is identified as GL(4,2), showcasing its structure.
Methods of point-line geometries unveil the automorphism groups of the remaining designs, enhancing understanding.
This research describes the group actions on points and blocks within these symmetric (15,8,4)-designs.
The findings contribute to the field of combinatorial designs, with implications for geometric configurations.

Abstract

It is clear that the full automorphism group of the (15, 8, 4) -design of points and hyperplane complements of PG (3, 2) is GL (4, 2). Using methods of point-line geometries, we determine the full automorphism groups of the remaining four symmetric (15, 8, 4) -designs and describe their actions on the sets of points and blocks.

The full automorphism groups of the five symmetric (15, 8, 4) -designs

Key Points

Abstract

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